Reconstructing pictures with machine learning [demonstration]¶
In this post I demonstrate how different techniques of machine learning are working.
The idea is very simple:
- each black & white image can be treated as a function of 2 variables - x1 and x2, position of a pixel
- intensity of a pixel is output
- this 2-dimentional function is very complex
- we can leave only a small fraction of pixels, treating others as 'lost'
- by looking how different regression algorithms reconstruct the picture, we can get some understanding of how these algorithms are operating
Don't treat this demonstration as some 'comparison of approaches', because this problem (reconstructing a picture) is very specific and has very few in common with typical ML datasets and problems. And of course, this approach is not to be used in practice to reconstruct pictures :)
I am using scikit-learn and making use of its API, enabling user to construct new models via meta-ensembling and pipelines.
# !pip install image from PIL import Image %pylab inline
Populating the interactive namespace from numpy and matplotlib
import numpy from sklearn.pipeline import make_pipeline from sklearn.ensemble import RandomForestRegressor, BaggingRegressor, GradientBoostingRegressor, AdaBoostRegressor from sklearn.cross_validation import train_test_split from sklearn.random_projection import GaussianRandomProjection from sklearn.tree import DecisionTreeRegressor from sklearn.linear_model import LinearRegression from sklearn.kernel_approximation import RBFSampler from sklearn.preprocessing import StandardScaler from sklearn.svm import SVR from sklearn.neighbors import KNeighborsRegressor from rep.metaml import FoldingRegressor from rep.estimators import XGBoostRegressor, TheanetsRegressor
!wget http://static.boredpanda.com/blog/wp-content/uploads/2014/08/cat-looking-at-you-black-and-white-photography-1.jpg -O image.jpg # !wget http://orig05.deviantart.net/1d93/f/2009/084/5/2/new_york_black_and_white_by_morgadu.jpg -O image.jpg
--2016-02-16 15:40:20-- http://static.boredpanda.com/blog/wp-content/uploads/2014/08/cat-looking-at-you-black-and-white-photography-1.jpg Resolving static.boredpanda.com... 22.214.171.124 Connecting to static.boredpanda.com|126.96.36.199|:80... connected. HTTP request sent, awaiting response... 200 OK Length: 80728 (79K) [image/jpeg] Saving to: 'image.jpg' image.jpg 100%[=====================>] 78.84K --.-KB/s in 0.05s 2016-02-16 15:40:20 (1.41 MB/s) - 'image.jpg' saved [80728/80728]
image = numpy.asarray(Image.open('./image.jpg')).mean(axis=2) plt.figure(figsize=[20, 10]) plt.imshow(image, cmap='gray')
<matplotlib.image.AxesImage at 0x1184b6150>
Define a function to train regressor¶
train_size is how many pixels shall be used in reconstructing the picture. By default, the algorithm will use only 2% of pixels
def train_display(regressor, image, train_size=0.02): height, width = image.shape flat_image = image.reshape(-1) xs = numpy.arange(len(flat_image)) % width ys = numpy.arange(len(flat_image)) // width data = numpy.array([xs, ys]).T target = flat_image trainX, testX, trainY, testY = train_test_split(data, target, train_size=train_size, random_state=42) mean = trainY.mean() regressor.fit(trainX, trainY - mean) new_flat_picture = regressor.predict(data) + mean plt.figure(figsize=[20, 10]) plt.subplot(121) plt.imshow(image, cmap='gray') plt.subplot(122) plt.imshow(new_flat_picture.reshape(height, width), cmap='gray')